This invention relates to an apparatus for controlling an adjustable speed electric motor and, more particularly, to an apparatus for vector control of an induction motor.
Electric power converters or inverters have been employed for the application of adjustable speed drives using alternating current motors. A typical converter includes a direct current (DC) rectifier for rectifying three-phase AC input voltage and for supplying the resulting direct current (DC) bus potential to an inverter. The inverter comprises a plurality of pairs of series-connected switching elements to generate an adjustable frequency output. In many applications, such a frequency adjustment is effected through a control circuit which employs a pulse width modulation (PWM) control technique in producing variable frequency gating pulses to periodically switch the respective switching elements so as to operate the motor at a variable speed. The motor can be propelled (motoring mode) or retarded (braking mode) as desired by appropriately varying the frequency and the amplitude of the excitation that the inverter applies to the motor.
The actual motor speed is sensed and compared with a commanded motor speed. An speed error signal, which depends on the difference between the actual and desired values of motor speed, is derived and applied to a proportional-plus-integral control circuit which converts it into a torque command signal. The control circuit responds to the torque command signal by controlling the operation of the inverter so as to vary, as a function of the torque command signal, the amplitude of the voltages supplied from the inverter to the motor.
In order to provide more accurate motor control, vector control has been proposed and employed to control the momentary value of the stator current of the induction motor to generate a torque. Slip frequency type vectro control employs an induction motor secondary resistance (secondary time constant) in calculating a slip frequency as: EQU .omega..sub.s =(1/.tau..sub.2 *).times.(i.sub.1.beta. */i.sub.1.alpha. *)
where .tau..sub.2 is the secondary time constant, i.sub.1.alpha. is the excitation current, i.sub.1.beta. * is the torque current. This equation is obtained when a coordinate system is used which coincides with the power phase of the power source. The factors used in calculations are suffixed by the symbol *.
In steady conditions, the and .beta. components .lambda..sub.2.alpha. and .lambda..sub.2.beta. of the secondary flux are represented as: EQU .lambda..sub.2.alpha. =M.times.i.sub.1.alpha. *.times.(1+KI.sup.2)/{1+(KI).sup.2 } EQU .lambda..sub.2.beta. =M.times.i.sub.1.beta. *.times.(1-K)/{1+(KI).sup.2 }
where M is the mutual inductance of the induction motor, K is the ratio of .tau..sub.2 /.tau..sub.2 *, and I is the ratio of i.sub.1.beta. */i.sub.1.alpha. *.
As can be seen from the equations, the .beta. component of the secondary flux is not zero, resulting in improper vector control when the secondary time constant .tau..sub.2 * used in calculating the slip frequency is different from the actual secondary time constant .tau..sub.2 (or K.noteq.1). When the secondary flux contains a .beta. component, the torque Te of the induction motor is represented as: EQU Te=K.sub.T .times.(.lambda..sub.2.alpha. .times.i.sub.1.beta. -.lambda..sub.2.beta. .times.i.sub.1)
where K.sub.T is a constant represented as K.sub.T =P.times.M.sup.2 /L.sub.2, P is the pole number, and L.sub.2 is the secondary inductance.
The secondary resistance (secondary time constant) varies by a factor of 1.5 from its initially set value due to ambient temperature changes, load changes, and induction motor secondary conductor temperature changes. The influence of the deviation of the secondary time constant from its actual value is serious particularly for inverters of current control type.